A relativistic electron beam with velocity v(b)(z) over cap passing over a
metallic grating, with deep periodic depressions of wavenumber k(0)(z) over
cap, excites a slow wave (omega, k(z)) via Cerenkov interaction, omega = (
k(2) + k(0))v(b). The beam bunches induce currents in the fins of the grati
ng that act as a phased radiating dipole array, thereby generating coherent
radiation at a wavelength lambda = (2 pi/k(0)l)(c/v(b) - sin theta) where
l is an integer and theta is the angle of emission measured from the normal
of the grating, The current threshold for the instability and radiation po
wer scaling with beam current are discussed.